An important feature of living active matter is the presence of birth and death where the ratio of birth and death rates can lead to three distinct implications on the overall system size or total number of particles: (i) when birth rate is less than the death rate, (ii) birth and death rates are balanced and (iii) when birth rate is in excess of the death rate. In this work we focus on the third scenario where birth rate exceeds the death rate leading to a fast expanding collection of active particles with boundary growth. Study of growth and fluctuation of interfaces between one medium and another have laid the groundwork for important advances in physics. For instance, the Kardar-Parisi-Zhang(KPZ) model describes the stochastic growth profile of interfaces [1]}, elucidating the behavior of materials ranging from crystal growth in thin films, turbulent liquid crystals to bacterial colony growth [2]}. In the KPZ model, the particle flux is orthogonal to the growing interface whereas another interesting scenario deals with particle flux generated by the surface itself as is relevant in biological systems such as membranes and cell collectives [3]}, [4]}, [5]}. In this context, Risler et. al. [6]} described the out-of-equilibrium surface fluctuations of cell collectives in the homeostatic state when cell birth and death are balanced. Building on our prior work [7]}, [8]}, [9]}, [10]}, [11]} where we modeled biological cells with pairwise elastic and adhesive interaction in addition to rules for size growth, division and death of particles, we study the surface roughness of a dense and fast expanding three dimensional (3D) collection of active particles. We focus on investigating 3D aggregate expansion at varying inter-particle adhesion strengths, known to critically tune collective properties in active matter systems. Our study models a dense 3D active particle aggregate expanding into a highly viscous surrounding medium, under free boundary conditions in the context of an off-lattice model.
